Hyperspectral Anomaly Detection Fused Unified Nonconvex Tensor Ring Factors Regularization

2025-05-23

AI Summary

Existing hyperspectral anomaly detection (HAD) methods struggle to simultaneously capture the global spatial-spectral correlations and local smoothness of background components. To address this, we propose HAD-EUNTRFR, a novel tensor-based framework that decomposes hyperspectral imagery into background and anomaly components. The background is modeled via tensor ring decomposition (TRD) to characterize its global spatial-spectral structure, while a unified non-convex tensor ring factor regularization—first introduced herein—jointly enforces low-rankness and 3D gradient sparsity. Anomalies are modeled using a generalized non-convex penalty to capture their group-sparse structure. The optimization is efficiently solved via truncated singular value decomposition (TSVD) and the alternating direction method of multipliers (ADMM). Extensive experiments on multiple benchmark datasets demonstrate significant improvements over state-of-the-art methods in detection accuracy, while maintaining strong interpretability and computational efficiency.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Other Foundations of Computer Vision
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

In recent years, tensor decomposition-based approaches for hyperspectral anomaly detection (HAD) have gained significant attention in the field of remote sensing. However, existing methods often fail to fully leverage both the global correlations and local smoothness of the background components in hyperspectral images (HSIs), which exist in both the spectral and spatial domains. This limitation results in suboptimal detection performance. To mitigate this critical issue, we put forward a novel HAD method named HAD-EUNTRFR, which incorporates an enhanced unified nonconvex tensor ring (TR) factors regularization. In the HAD-EUNTRFR framework, the raw HSIs are first decomposed into background and anomaly components. The TR decomposition is then employed to capture the spatial-spectral correlations within the background component. Additionally, we introduce a unified and efficient nonconvex regularizer, induced by tensor singular value decomposition (TSVD), to simultaneously encode the low-rankness and sparsity of the 3-D gradient TR factors into a unique concise form. The above characterization scheme enables the interpretable gradient TR factors to inherit the low-rankness and smoothness of the original background. To further enhance anomaly detection, we design a generalized nonconvex regularization term to exploit the group sparsity of the anomaly component. To solve the resulting doubly nonconvex model, we develop a highly efficient optimization algorithm based on the alternating direction method of multipliers (ADMM) framework. Experimental results on several benchmark datasets demonstrate that our proposed method outperforms existing state-of-the-art (SOTA) approaches in terms of detection accuracy.

Problem

• Improves hyperspectral anomaly detection by leveraging global and local correlations
• Introduces nonconvex tensor ring regularization for background and anomaly separation
• Enhances detection accuracy via efficient optimization and group sparsity

Innovation

• Enhanced unified nonconvex tensor ring regularization
• TSVD-induced low-rank sparse gradient factors
• ADMM-based optimization for nonconvex model